How does necessary inference work? It first begins with a passage. For this example, let us consider Psalm 110:4.
In this passage, God swears that the one mentioned in verse 1 as David's lord will be a priest forever after the order of Melchizedek. When this passage is combined with other passages pertaining to the Messiah such as Zechariah 6:13 and 2 Samuel 7:12, we discover that the Messiah was to be of the lineage of David and that He would be both King and Priest.
Well this poses a problem. David was part of the tribe of Judah. The priests were descendants of Aaron, the brother of Moses and were of the tribe of Levi. It was not lawful under the Law given at Mt. Sinai through Moses for a member of the tribe of Judah to be a priest.
Furthermore, Psalm 110:4 does not say - a priest after the order of Aaron - but rather it says - "a priest after the order of Melchizedek.
This meant that the Messiah's priesthood would not be based on Aaron's priesthood and that the Law would have to be changed in order for the Messiah of the tribe of Judah to lawfully be a priest.
In fact this is exactly what the writer of the epistle to the Hebrews argues in Hebrews 7:11-16.
The Hebrew writer bases his argument on a logical analysis of the consequences of Psalm 110:4.
The next web page contains an explanation of the layout of the charts on this website
A Look At A Method of Logic Used In The New Testament